A164110 - OEIS

%I #9 Sep 08 2022 08:45:47

%S 5,36,262,1920,14132,104304,771160,5707584,42271568,313200960,

%T 2321178208,17205305856,127543611200,945542935296,7010032442752,

%U 51971929512960,385322051101952,2856819009782784,21180878379927040

%N a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 5, a(1) = 36.

%C Binomial transform of A164038. Sixth binomial transform of A164095.

%H Vincenzo Librandi, <a href="/A164110/b164110.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-34).

%F a(n) = ((5+3*sqrt(2))*(6+sqrt(2))^n+(5-3*sqrt(2))*(6-sqrt(2))^n)/2.

%F G.f.: (5-24*x)/(1-12*x+34*x^2).

%F E.g.f.: (5*cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x))*exp(6*x). - _G. C. Greubel_, Sep 11 2017

%t LinearRecurrence[{12,-34}, {5,36}, 50] (* _G. C. Greubel_, Sep 11 2017 *)

%o (Magma) [ n le 2 select 31*n-26 else 12*Self(n-1)-34*Self(n-2): n in [1..19] ];

%o (PARI) x='x+O('x^50); Vec((5-24*x)/(1-12*x+34*x^2)) \\ _G. C. Greubel_, Sep 11 2017

%Y Cf. A164038, A164095.

%K nonn

%O 0,1

%A _Klaus Brockhaus_, Aug 10 2009